1. Field of the Invention
The present invention concerns, generally speaking, digital filtering and centers around a recursive digital filter which delivers, from digitized samples of an analog input signal, a series of numbers representing the digitized values of the filtered analog signal. More particularly, the invention concerns low-pass, high-pass or rejection recursive digital filters the recurrence relationship coefficients of which are formed by a small number of combinations of powers of two.
In accordance with a preferred embodiment of the invention, the recursive digital filter is a second order filter of the Butterworth type with a damping coefficient .eta. equal to 1/.sqroot.2, Another preferred embodiment refers to a first order recursive digital filter with coefficients of powers of two.
A further preferred embodiment concerns second order recursive digital filters in which the coefficients of the recurrence relationship of the filter are expressed in the form of sums of a small number of terms equal to a power of two and in which the damping factor .eta. can equal in particular, 0, 1/2, 1/.sqroot.2 and 1, and more generally 2.sup.k/2 where k is an integer.
Other embodiments of the present invention make it possible to perform the synthesis of various types of filters such as, for example, those of Bessel, Legendre or Tchebyscheff.
The recursive digital filters of the invention with power of two coefficients have filtering rates in real time a thousand times faster than those achieved by means of conventional minicomputers equiped with a wired or microprogrammed floating point calculation module.
The time required by the filters of the invention to calculate a filtered point is of the order of a few hundreds of nanoseconds which allows an increased rate of the analog input signal sampling and minimizes the influence of spectrum overlap. The low calculation time also allows several digital filter modules of a similar or of differing types to be placed in series enabling transfer functions of a more general nature to be obtained.
The filters on the invention can advantageously replace analog filters when the necessary cut-off frequencies are very low. In actual fact, on the strength of their performance, ease of development and cost price, they should find a wide range of applications wherever the characteristics of analog filters prove to be insufficient, which is essentially the case of low-pass filtering with very low cut-off frequencies.
The low-pass filtering of measuring signals is poorly resolved by analog filters when cut-off frequencies drop below 1 Hz. The analog filters available for these frequencies lack stability and are not easily reproducible as regards phase response; moreover, the cost price is high. Digital filters, on their other hand, are well suited to the filtering of very low frequencies: they do not drift and, for a given calculation algorithm, present a perfectly defined phase response.
A digital filter can operate either in delayed time or in real time. It is said to operate in real time if the calculation of a filtered point at a given moment in time only resorts to input analog signal samples corresponding to previous moments in time or equal to the given moment. Furthermore, the calculation time of a filtered point must be less than the sampling period. The advantage of operating in real time is apparent, for instance, in the reduction of the volume of data to be transmitted to a central data processing computer, or else in the possibility of including the data acquisition and pre-processing system in a control loop.
It is a known fact that if it is desired to sample a signal at a sampling frequency f.sub.e, the signal to be sampled should not contain any frequency components greater than f.sub.e /2 so as to obviate any spectrum overlap. It is thus essential, before sampling the signal and filtering it digitally, to conduct an analog prefiltering process in order to eliminate the signal components with frequencies greater than half the sampling frequency. By way of illustration, let us take the case of a second order low-pass analog pre-filtering stage with a cut-off frequency of 10 Hz and a -40 dB per decade attenuation. We then find that, to digitally filter frequency components of the signal with a given accuracy of 10.sup.-2, 10.sup.-3 or 10.sup.-4, for instance, we must maintain the frequencies below 100, 300 or 1000 Hz respectively in the analog pre-filtering stage. This imposes sampling frequencies, f.sub.e, of 200, 600 and 2000 Hz respectively.
2. Description of the Prior Art
E. Haziza and J. Appel's article entitled "The real time filtering of measurements carried out in the wind-tunnel" (NT Office National d'Etudes et de Recherches Aerospatiales, 3/7146 PY) shows to what extent a minicomputer used for measurement, data acquisition and storage is also capable of digitally filtering in real time the signals obtained. The programmed filter is a second order low-pass recursive filter and the digital filtering capacity in real time of the minicomputer is 8 measurement channels each one of which is sampled 200 times per second.
It is immediately obvious that when the desired accuracy level is high (10.sup.-4 for example) and the number of channels to be filtered is substantial (of the order of a few tens) such an acquisition and storage minicomputer is no longer able to carry out real time digital filtering conventionnally.